lean_workbook_plus_16640

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c \in \mathbb{R}$ such that $a+b+c=3$ . Prove that

\frac{a^3+b^3+c^3}{3} \geq 1+(a-1)(b-1)(c-1)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16640 (a b c : ℝ) (h : a + b + c = 3) :
  (a^3 + b^3 + c^3) / 3 ≥ 1 + (a - 1) * (b - 1) * (c - 1)   :=  by sorry

Source